Depending on the kind of wine, it can have between 1 and 10 grams of carbohydrates per serving. Dry white wines can have from one to two carbs per 5-ounce serving. At the high end of the spectrum, fortified wines like port can have as much as 10 carbs per 3-ounce serving.
All alcoholic drinks start out heavy in carbs, but, during the fermentation process, many of those carbs are broken down and eaten by the yeast to produce the actual alcohol content. Any sugars left over are what contribute to the amount of carbs, which varies from one type of drink to the other.